The Zipf Mystery

Every so often scientists notice a rule or a regularity that makes no particular sense on its face but seems to hold true nonetheless. One such is a curiosity called Zipf’s Law. George Kingsley Zipf was a Harvard linguist who in the 1930s noticed that the distribution of words adhered to a regular statistical pattern. The most common word in English—”the”—appears roughly twice as often in ordinary usage as the second most common word, three times as often as the third most common, ten times as often as the tenth most common, and so on. As an afterthought, Zipf also observed that cities’ sizes followed the same sort of pattern, which became known as a Zipf distribution. Oversimplifying a bit, if you rank cities by population, you find that City No. 10 will have roughly a tenth as many residents as City No. 1, City No. 100 a hundredth as many, and so forth. (Actually the relationship isn’t quite that clean, but mathematically it is strong nonetheless.) Subsequent observers later noticed that this same Zipfian relationship between size and rank applies to many things: for instance, corporations and firms in a modern economy are Zipf-distributed.